Two Classes of Exponentially Stabilizable LPV Systems
Bibliographic record
Abstract
Linear parameter-varying (LPV) systems, which have dynamics that vary according to a scheduling parameter, are capable of representing a wide variety of nonlinear and time-varying dynamics. The LPV paradigm preserves well-understood linear design methods, although the stability analysis of these systems has remained difficult. In a recent paper, it is shown that under some stringent conditions, a linear continuous-time gain-scheduled output feedback controller can be designed to provide closed-loop exponential stability; however, the conditions are hard to check, few examples are provided and all of the examples are stable. The goal of this article is to construct two large families of single-input single-output second-order systems, which satisfy these constraints while admitting wide ranges of parameter variation. The classes constructed include unstable and nonminimum phase systems, and consequently, this work facilitates the design of exponentially stabilizing LPV controllers for systems that are difficult to control.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".